1. Field of the Invention
The present invention relates to a musical tone synthesizing apparatus which is suitable for the electronic wind instrument.
2. Prior Art
Conventionally known technique can synthesize the musical tone of non-electronic musical instrument (hereinafter, simply referred to as acoustic instrument) by operating the artificial tone-generation model which is obtained by simulating the tone-generation mechanism of acoustic instrument. Such musical tone synthesizing technique is disclosed in Japanese Patent Laid-Open Publication No. 63-40199, for example. Hereinafter, description will be given with respect to the modeling of the above-mentioned tone-generation mechanism of the wind instrument, and thereafter description will be further given to the conventional musical tone synthesizing apparatus using such modeling.
FIG. 1 is a sectional view showing the diagrammatical construction of the wind instrument such as the clarinet, saxophone etc. In FIG. 1, 1 designates a resonance tube and 2 designates a reed. In addition, TH designates a tone hole (or sound hole) which is formed at the predetermined position of the resonance tube 1.
When the performer blows breath 2A into the reed 2, the reed 2 vibrates due to blowing pressure PA and elastic characteristic thereof in direction 2S. As a result, pressure wave (i.e., compression wave) of air is produced in the vicinity of the reed 2 within the tube 1. Then, such compression wave progresses toward a terminal portion 1E of the tube 1 as progressive compression wave F. This progressive compression wave F is reflected by the terminal portion 1E and then returned to the reed 2 as reflected compression wave R, so that the reed 2 is affected by pressure PR due to reflected compression wave R. Therefore, when blowing the wind instrument, the reed 2 is affected by the following pressure P. EQU P=PA-PR (1)
For this reason, the reed 2 will vibrate by the pressure P and elastic characteristic thereof- When the resonance state is established between the vibration of the reed 2 and the reciprocating motion of the compression waves F, R, the musical tone is generated from the wind instrument.
In this case, the resonance frequency is changed over by open/close operation of the tone hole TH formed at the tube 1. More specifically, when the open/close operation is carried out on the tone hole TH by the performer's finger, the flow of the compression wave is varied in the vicinity of the tone hole TH so that the substantial length of the tube is varied, whereby the resonance frequency is to be changed over.
FIG. 2 shows electric configuration of the conventional musical tone synthesizing apparatus which is obtained by simulating the tone-generation mechanism of the wind instrument. In FIG. 2, 11 designates a non-linear element which simulates the operation of the reed 2, 12 designates a resonance circuit which simulates the resonance tube 1, and 13 designates a subtractor which simulates the foregoing formula (1) to be operated by the reed 2. Herein, the output of the non-linear element 11 is applied to the resonance circuit 12 as progressive wave signal. Then, the resonance circuit 12 converts the progressive wave signal into reflected wave signal, which is supplied to the subtractor 13.
In the resonance circuit 12, BD.sub.1, BD.sub.2, . . . designate bi-directional transmission circuits each simulating the transmission delay characteristic of the compression wave which propagates in the resonance tube 1. In each of the bi-directional transmission circuits BD.sub.1, BD.sub.2 etc., DF designates a delay circuit for transmitting the progressive wave signal and DR designates another delay circuit for transmitting the reflected wave signal. Further, TRM designates a terminal circuit which simulates the reflection of the compression wave which is reflected at the terminal portion 1E of the resonance tube 1 (see FIG. 1). This terminal circuit TRM consists of a low-pass filter ML and an inverter IV. Herein, the low-pass filter ML simulates the acoustic loss which is occurred due to the reflection of the compression wave, while the inverter IV simulates the phase inversion of the compression wave to be reflected. Incidentally, this inverter IV is not requires when the terminal portion 1E is closed but required when the terminal portion 1E is opened.
Furthermore, JU.sub.1 designates a junction circuit which simulates the scattering of the compression wave in the vicinity of the tone hole TH. In JU.sub.1, M.sub.1, M.sub.2 designate multipliers; A.sub.1, A.sub.2 designate subtractors; and Aj designates an adder. The delay circuit DF in the bi-directional transmission circuit BD.sub.1 outputs progressive wave signal F.sub.1 to the multiplier M.sub.1 wherein F.sub.1 is multiplied by a coefficient a.sub.1 so that multiplication result a.sub.1 F.sub.1 is obtained. On the other hand, the delay circuit DR in the bi-directional transmission circuit BD.sub.2 outputs reflected wave signal R.sub.1 to the multiplier M.sub.2 wherein R.sub.1 is multiplied by another coefficient a.sub.2 so that multiplication result a.sub.2 R.sub.1 is obtained. Herein, the coefficients a.sub.1, a.sub.2 will be described later in detail. The adder Aj adds these two multiplication results together, and then its addition result is supplied to both of the subtractors A.sub.1, A.sub.2. The subtractor A.sub.1 subtracts F.sub.1 from the addition result of adder Aj to thereby output its subtraction result to the delay circuit DR in the bi-directional transmission circuit BD.sub.1 as reflected wave signal R.sub.2. On the other hand, the subtractor A.sub.2 subtracts R.sub.1 from the addition result of Aj to thereby output its subtraction result to the delay circuit DF in the bi-directional transmission circuit BD.sub.2 as progressive wave signal F.sub.2.
Next, description will be given with respect to the coefficients a.sub.1, a.sub.2 to be used in the multipliers M.sub.1, M.sub.2 with respect to two cases.
(i) First Case where the tone hole TH is opened:
The following formula (2) represents air pressure Pj at point j which is set in the vicinity of the tone hole TH in the tube 1 shown in FIG. 1. EQU Pj=a.sub.1 off P.sub.1+ +a.sub.2 off P.sub.2+ ( 2)
Herein, P.sub.l+ designates the pressure of the compression wave which enters into the point j from the reed 2, while P.sub.2+ designates another pressure of the compression wave which enters into the point j from the terminal portion 1E. In addition, a.sub.1 off, a.sub.2 off designate ratios of two pressures of compression waves, which can be represented by the following formulae (3), (4) respectively. EQU a.sub.1 off=2.phi..sub.1.sup.2 /(.phi..sub.1.sup.2 +.phi..sub.2.sup.2 +.phi..sub.3.sup.2) (3) EQU a.sub.2 off=2.phi..sub.2.sup.2 /(.phi..sub.1.sup.2 +.phi..sub.2.sup.2 +.phi..sub.3.sup.2) (4)
In the above formulae, .phi..sub.1 designates the diameter of the tube 1 in reed side; .phi..sub.2 designates the diameter of the tube 1 in terminal side; and .phi..sub.3 designates the diameter of the tone hole TH. In FIG. 2, the progressive wave signal F.sub.1 corresponds to the pressure P.sub.1+, while the reflected wave signal R.sub.1 corresponds to the pressure P.sub.2+. In this first case where the tone hole TH is opened, the above-mentioned coefficients a.sub.1 off, a.sub.2 off are used as the foregoing coefficients a.sub.1, a.sub.2 of the multipliers M.sub.1, M.sub.2 respectively. For this reason, the adder Aj can output the operation result of foregoing formula (2), i.e., signal corresponding to the air pressure Pj at the point j in the tube 1.
Meanwhile, the following formulae (5), (6) respectively represent pressure P.sub.1- of the reflected compression wave which flows from the point j toward the reed 2 and pressure P.sub.2- of the progressive compression wave which flows from the point j toward the terminal portion 1E. EQU P.sub.1- =Pj-P.sub.1+ ( 5) EQU P.sub.2- =Pj-P.sub.2+ ( 6)
Thus, these pressures P.sub.1-, P.sub.2- correspond to the outputs of the subtractors A.sub.1, A.sub.2 respectively.
(ii) Second Case where the tone hole TH is closed:
This case is equivalent to the state where the diameter .phi..sub.3 of the tone hole TH is at "0". Therefore, coefficients a.sub.1 on, a.sub.2 on can be obtained by putting ".phi..sub.3 =0" in the foregoing formulae (3), (4) respectively. EQU a.sub.1 on=2.phi..sub.1.sup.2 /(.phi..sub.1.sup.2 +.phi..sub.2.sup.2)(7) EQU a.sub.2 on=2.phi..sub.2.sup.2 /(.phi..sub.1.sup.2 +.phi..sub.2.sup.2)(8)
These coefficients a.sub.1 on, a.sub.2 on are used as the foregoing coefficients a.sub.1, a.sub.2 of the multipliers M.sub.1, M.sub.2.
Thus, the adder Aj can output the signal corresponding to the air pressure Pj at the point j of the tube 1 in accordance with the following formula (9). EQU Pj=a.sub.1 onP.sub.1+ +a.sub.2 onP.sub.2+ ( 9)
Then, the subtractors A.sub.1, A.sub.2 output signals corresponding to the pressures P.sub.1-, P.sub.2-.
As described heretofore, the circuit shown in FIG. 2 can simulate the scattering state of the compression wave in the tube 1 in response to the open/close operation of the tone hole TH.
In the present example of the conventional musical tone synthesizing apparatus, a bias value VA corresponding to the blowing pressure PA is applied to the non-linear element 11 via the subtractor 13. The output signal of the non-linear element 11 is transmitted to the terminal circuit TRM via the bi-directional transmission circuits BD.sub.1, BD.sub.2 and junction circuit JU.sub.1 etc. In the junction circuit JU.sub.1, values of the coefficients a.sub.1, a.sub.2 are changed over in response to the open/close operation of the tone hole TH as described before, and consequently the scattering state in the junction circuit JU.sub.1 is changed over. The progressive wave signal reached at the terminal circuit TRM is processed by the low-pass filter ML and inverter IV so that the reflected wave signal is obtained. This reflected wave signal is transmitted through the circuits BD.sub.2, JU.sub.1, BD.sub.1 etc. and then supplied to the non-linear element 11 via the subtractor 13. Thus, the resonance state is established between the non-linear element 11 and resonance circuit 12. In this case, the resonance frequency can be changed over by changing over the coefficients a.sub.1, a.sub.2 used in the junction circuit JU.sub.1 in response to the open/close state of the tone hole TH.
In the actual performance of the wind instrument, the tone hole is gradually opened or closed by the performer's finger. However, the junction circuit of the above-mentioned conventional musical tone synthesizing apparatus can merely change over its operation in response to full-open and full-close states of the tone hole TH. For this reason, there is a problem in that the conventional apparatus cannot reproduce the real variation of the musical tone in response to the finger operation of the wind instrument.
Meanwhile, some wind instrument provides the tone hole portion which is projected from the tube as shown in FIG. 5. In such case, the compression wave is partially and discretely flown into the opening portion of the tone hole, and the compression wave is partially reflected by the opening portion of the tone hole. However, the conventional apparatus cannot simulate such projection of the tone hole portion. For this reason, there is a problem in that the conventional apparatus cannot simulate the wind instrument with accuracy.
In addition, the conventional apparatus as shown in FIG. 2 requires one junction circuit (including two multipliers, two subtractors and one adder) in order to carry out the operational process which simulates the operation of one tone hole. Therefore, there is a problem in that the hardware of the conventional apparatus must be enlarged. In contrast, when the above-mentioned operational process is carried out by the software to be executed by the digital signal processor (DSP) and the like, there is a problem in that the amount of software operations must be increased.